Euler, φ and ρ

[Note: I need to end the equations with a period to persuade WordPress/Latex to put sane spacing between lines.

Euler’s famous equation e^{iπ} + 1 = 0 is usually considered the “most beautiful” in mathematics.

We could also write it in the so-called “ugly” format as e^{iπ} = -1.

Now we know that for the golden ratio φ,

{1 \over {φ}} - φ = -1.

So let’s rewrite Euler using that:

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